Method for tuning choke operation in a managed pressure drilling system

ABSTRACT

A method for tuning a managed pressure drilling system comprising a variable orifice choke to control fluid flow from a drilling well includes (a) characterizing change in flow rate through the choke with respect to choke opening at a substantially constant pressure drop; (b) characterizing change in fluid pressure in the well with respect to change in choke opening at a substantially constant flow rate into the well; (c) characterizing a response time of pressure in the well to changes in the choke opening, a delay time of pressure response after a change in choke opening and a back pressure applied to the well with respect to choke opening. The characterizations in at least one of (a) and (b), and the characterization in (c) are used as control parameters for a proportional integral differential controller having as output the choke opening and as input the fluid pressure in the well before the choke.

CROSS REFERENCE TO RELATED APPLICATIONS

Continuation of International Application No. PCT/US2021/026402 filed on Apr. 8, 2021. Priority is claimed from U.S. Provisional Application No. 63/009,097 filed on Apr. 13, 2020. Both the foregoing applications are incorporated herein by reference in their entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT

Not Applicable.

BACKGROUND

This disclosure relates to the field of flow control devices (“chokes”) used in well drilling. More specifically, the disclosure relates to chokes used during drilling operations for managing pressure in a well annulus.

Managed pressure drilling is used to maintain drilling fluid pressure in the well annulus (the space between open formations and a drilling tool “string”) of a drilling well within a range between exposed formation fluid (“pore”) pressure and exposed formation mechanical failure (“fracture”) pressure. The difference between the foregoing pressures is known as a pressure window, is sometimes referred to as the “drilling margin” and represents the pressure range within which little or no formation fluids are drawn into the well and little or no drilling fluids are lost to the exposed formations. While drilling fluids are typically weighted (made more dense than plain water and/or oil to exert higher pressure), other factors including fluid friction, pipe rotation, and applied surface back pressure (“ASBP”) contribute to the effective fluid pressure acting on the exposed formations. Failure to precisely control the foregoing variables can result in a well control event, including the unintentional influx of formation fluids into the wellbore or the loss of expensive drilling fluids to the formation. Consequently, allowing fluid pressure to fall outside the drilling margin can substantially increase drilling costs and expose the drilling rig and personnel to dangerous conditions including, potentially, a blowout (uncontrolled influx of fluid into the well).

Managed pressure drilling (“MPD”) systems seal the annulus surrounding the drill string for all operations, including rotating and stripping operations, and improve the ability of equipment on the drilling unit (“rig”) to manage well annulus pressure. With the wellbore sealed, MPD systems allow for the application of “surface back pressure” to the well, namely, fluid pressure applied from equipment at the surface to the well annulus. The drilling rig operator may cause the MPD system to apply additional surface back pressure to increase the pressure overbalance acting on the exposed formations, or he may drill ahead with back pressure and relatively less dense drilling fluid to allow for rapid downward bottom hole pressure adjustment to mitigate fluid losses. During connections (assembly and disassembly of segments of drilling pipe and/or tools to change the length of the tool string), surface back pressure may be increased to offset the loss of pressure otherwise resulting from circulation-caused friction that occurs when the drilling fluid (mud) pumps are stopped. Typically, pressure is increased during connections when the mud pumps are stopped by an amount proportional to the difference between the equivalent circulating density (“ECD”) or equivalent well pressure including fluid friction pressure, and the equivalent static density (“ESD”) or equivalent well pressure with no fluid friction pressure.

MPD systems may allow the drilling rig operator to more quickly detect warning signs of a potentially hazardous situation. With the well annulus closed as explained above, all returning fluids from the well may be measured with greater accuracy, enabling faster fluid influx and loss detection than is available using conventional drilling techniques. Faster detection and response time may result in a smaller influx because the duration of the underbalanced condition is reduced. Smaller influxes are typically easier to circulate out of the well because there is typically less gas or light annular fluids that place less stress on weaker formations. In the event an unintentional influx is taken into the wellbore, MPD systems may be used to apply surface back pressure to the well to stop the influx before shutting the blowout preventer (“BOP”), which eliminates drawdown pressure acting on the formation following mud pump shutdown and closure of the BOP and further reduces the influx volume.

Conventional MPD systems include an annular sealing system, a drill string isolation tool, and a flow spool, or equivalents thereof that actively manage wellbore pressure during drilling and other operations. The annular sealing system may include a rotating control device (“RCD”), an active control device (“ACD”), or other type of annular sealing device that is configured to seal the annulus surrounding the drill pipe while it rotates and moves axially. The annulus is thus encapsulated such that it is not exposed to the atmosphere. The drill string isolation tool is usually disposed directly below the annular sealing system and includes an annular packer that encapsulates the well and maintains annular pressure when rotation has stopped and the annular sealing system, or components thereof, are being installed, serviced, removed, or otherwise disengaged. The flow spool is usually disposed directly below the drill string isolation tool and, as part of the pressurized fluid return system, diverts fluids from below the annular seal to the surface. The flow spool is in fluid communication with a choke manifold, typically disposed on a platform of the drilling rig that is in fluid communication with a mud-gas separator, shakers, or other fluids processing system. The pressure tight seal on the annulus allows for the precise control of wellbore pressure by manipulation of the choke settings of the choke manifold and the corresponding application of surface back pressure.

One or more variable orifice chokes in the choke manifold may be operated automatically in response to measurements of one or more parameters having a relationship to the annulus pressure, for example and without limitation flow rate of fluid out of the well. Automating operation of the one or more variable orifice chokes requires tuning or calibrating of the choke orifice with respect to annulus fluid pressure for each set of well drilling equipment specifications, well depth, well diameter and drilling fluid rheological properties among other parameters.

SUMMARY

One aspect of the present disclosure is a method for tuning a managed pressure drilling system comprising a variable orifice choke to control fluid flow from a drilling well includes (a) characterizing change in flow rate through the choke with respect to choke opening at a substantially constant pressure drop; (b) characterizing change in fluid pressure in the well with respect to change in choke opening at a substantially constant flow rate into the well; (c) characterizing a response time of pressure in the well to changes in the choke opening, a delay time of pressure response after a change in choke opening and a back pressure applied to the well with respect to choke opening. The characterizations in at least one of (a) and (b), and the characterization in (c) are used to calculate control parameters for a proportional integral differential controller having as output the choke opening and as input the fluid pressure in the well before the choke.

In some embodiments, the characterizing change in flow rate of fluid through the choke with respect to fractional choke opening at a substantially constant pressure drop across the choke comprises pumping fluid through a conduit extended into the well, measuring flow rate of fluid leaving the well through an annular space between the conduit and a wall of the well, measuring pressure of fluid in the well upstream of the choke, adjusting the fractional choke opening and changing a rate of the pumping fluid so that the measured pressure remains substantially constant.

In some embodiments, the characterizing a response time of pressure in the well to changes in the fractional choke opening, a delay time of pressure response after a change in fractional choke opening and a surface back pressure applied to the well with respect to fractional choke opening comprises measuring pressure in the well upstream of the choke, measuring pressure upstream of the choke, and change in the measured pressure with respect to change in the fractional choke opening while pumping fluid into the well at a substantially constant rate.

In some embodiments, the characterizing a response time of pressure in the well to changes in the fractional choke opening comprises measuring pressure in the well upstream of the choke with respect to time, and determining an elapsed time between change in the fractional choke opening and a change in the measured pressure while pumping fluid into the well at a substantially constant rate.

Other aspects and possible advantages will be apparent from the description and claims that follow.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example embodiment of a managed pressure drilling (MPD) system.

FIG. 2 shows an example embodiment of an automatic choke.

FIG. 3 shows an example embodiment of a control system.

FIG. 4 shows a graph of an example well system response to changes in pressure.

FIG. 5 shows a graph of an example choke response with respect to position or opening.

FIG. 6 shows an example sensitivity curve for a choke.

FIG. 7 shows identifiable regions within a choke response as in FIG. 5 .

FIG. 8 shows a graph of an example embodiment of choke “fingerprinting.”

FIG. 9 shows a graph defining parameters used in choke characterization.

DETAILED DESCRIPTION

An example embodiment of a managed pressure drilling (MPD) system that may be used in accordance with a method of the present disclosure will be explained with reference to FIGS. 1 through 3 . It is to be clearly understood that the example embodiment of MPD system shown herein is only for purposes of illustration. Other embodiments of MPD system may be used in accordance with the present disclosure with equal effect.

Referring to FIGS. 1-3 , reference numeral 100 refers, in general, to an embodiment of a system (e.g., an MPD system) for controlling the fluid pressures within an oil or gas well 10. The system 100 includes an automatic choke 102 for controllably releasing pressurized fluids from an annular space (“annulus”) 24 between a wellbore casing 16 (and open drilled well below the casing 16, not shown) and drill pipe 18. Fluid (e.g., drilling mud) is pumped from a mud tank 20 by mud pump(s) 22 into the drill pipe 18. The fluid leaves the bottom of the drill pipe 18 and moves into the annulus 24. The annulus 24 is closed by a rotating control device 26 or similar annular seal.

The fluid is released from the annulus 24 through an automatic choke 102 which controllably restricts the outflow thereby to create back pressure within the wellbore 12. The outflow ultimately moves from the choke 102 to a mud tank 20. A control system 104 controls the operation (i.e., the effective orifice size) of the automatic choke 102 to maintain a selected pressure in the wellbore 12. The control system 104 may be in signal communication with a display and operator control panel 34 wherein control signals may be entered by a system operator, and system response may be observed.

A pressure sensor 32 a may measure pressure in the wellbore casing 16 (CSP). Another pressure sensor 32 b may measure pressure in the drill pipe (DPP) or stand pipe (SPP). A flow meter such as a Coriolis flow meter 106 may measure fluid flow out of the casing 16 and into the choke 102. Another flowmeter 108 may measure fluid flow rate into the drill pipe 18. The other flow meter 108 may be substituted by or supplemented with a stroke counter on the drilling unit mud pump(s) 22. The foregoing sensors may be in signal communication with the control system 104. Some embodiments may include a sensor 32 c that can measure pressure proximate the bottom of the wellbore 12, for example, a pressure while drilling (PWD) sensor. Such sensor 32 c may provide the advantage of certainty in determining in-wellbore pressure under dynamic conditions, however such sensor 32 c is not a requirement in order to operate the MPD system according to the present disclosure.

As illustrated in FIG. 2 , the automatic choke 102 may comprise a movable valve element 102 a that defines a continuously variable flow path resistance depending upon the position of the movable valve element 102 a. The position of the movable valve element 102 a may controlled by a first control pressure signal 102 b, and an opposite acting, second control pressure signal 102 c. In the illustrated example embodiment, the first control pressure signal 102 b may be representative of a set point pressure (SPP) that is generated by the control system 104, and the second control pressure signal 102 c is representative of the fluid pressure inside the casing 16 (CSP). In this manner, if the CSP is greater than the SPP, pressurized fluid within the annulus 24 of the well 10 is bled off at a greater rate into the mud tank 20 by increasing the choke 102 orifice. Conversely, if the CSP is equal to or less than the SPP, then the pressurized fluidic materials within the annulus 24 of the well 10 are bled off more slowly, by decreasing the choke 102 orifice, into the mud tank 20. In this manner, the automatic choke 102 provides pressure regulation than can controllably bleed off pressurized fluids from the annulus 24 and thereby also controllably create and maintain back pressure in the wellbore 12. In an example embodiment, the automatic choke 102 may be further provided substantially as described in U.S. Pat. No. 6,253,787 issued to Suter et al., which is incorporated herein by reference in its entirety

Thus, the system 100 may enable the CSP to be automatically controlled by the human system operator 104 c selecting the desired SPP. The automatic choke 102 then regulates the CSP as a function of the selected SPP.

The illustrated embodiment herein may be implemented in the form of pressure transducers for measuring SPP and CSP, and the control system 104 may be implemented in the form of a programmable logic controller, floating point gate array, application specific integrated circuit or any other microcomputer, computer, computer processor or controller known in the art. Accordingly, the embodiment explained above is not a limitation on the scope of the present disclosure.

In the most general terms, controlling pressure in the annulus is performed by controlling position of the automatic choke 102 in response to measurements of pressure and flow of drilling fluid (mud) into and/or out of the wellbore 12. A method according to the present disclosure has as an objective the calibration or “tuning” of the pressure control response of the MPD system, and in particular operation of the control system 104 as to its control of the automatic choke 102 in order to more precisely maintain well pressure under foreseeable operating conditions during drilling.

MPD System and Well Characteristics on a Drilling Well

The pressure response of most drilling wells to changes in fluid flow and/or choke opening can be approximated by a first order system having a time delay. Such wells are known as “open loop stable” (refer to the graph of FIG. 4 for an example). Open loop stable means that if a change in choke opening (position) is made, the pressure in the well will change correspondingly without going out of bounds or predetermined limits, if the choke opening is itself within reasonable limits. This characteristic may be used to predict an initial set of stable proportional integral differential (PID) control loop parameters.

The graph in FIG. 4 shows the pressure in the annulus (the “upstream” side of the choke 102 in FIG. 1 ) with reference to time, beginning at an arbitrary baseline pressure (ordinate axis=0). A choke position change is entered by the operator into the control system (104 in FIG. 1 ) at time t=0. The pressure as measured on the annulus side of the choke is indicated by curve 401. Note that a localized peak, at 403, in the actual well pressure response shown in FIG. 4 is due to characteristics of the MPD system surface equipment and is not due to well characteristics. This peak 403 is characteristic for marine (offshore) MPD operations and is commonly encountered. In determining the parameters of the well for choke tuning according to the present disclosure the peak 403 shown in FIG. 4 may be disregarded. The theoretical well pressure response is shown at curve 402.

The choke's flow characteristic is usually not linear but follows an approximate sigmoid function. This means that a nominal change, e.g., a nominal fractional step change in choke opening, does not result in a corresponding nominal flow variation over the entire range of choke opening. This is a well-known characteristic of chokes.

FIG. 5 shows a graph of characteristic flow for a choke, called Cv, at curve 501. Cv may be presented in units of flow rate of the choke at a specified pressure drop (in this case 1.0 pounds per square inch) for a particular fluid; in many cases for commercial characterization, pure water at 60 degrees Fahrenheit is used for characterization. Expressed as a formula:

Cv=Q√{square root over (SG/ΔP)}

wherein Q represents flow rate, ΔP represents pressure drop across the choke and SG represents the fluid's specific gravity. The coordinate axis, in fractional opening of the choke, from fully closed to fully open, is expressed in units of percent choke opening. The change in Cv for a 10 percentage point change in choke opening is shown at different points along the full range of choke opening, in the present case 30 to 40% opening, and 60 to 70% opening, compared to a linear curve, at 502, superimposed on the graph of FIG. 5 . Note that although the absolute change in Cv is more for the 60% to 70% opening change, the relative change for a step from 30% to 40% is much larger. Therefore the reaction of the pressure with respect to choke position changes will be more pronounced at smaller choke openings. Some commercially available PID loop models recognize the foregoing and allow two PID loop parameter sets to be defined so that optimal choke performance is achieved over the majority of the opening range of the choke. Sensitivity of the choke (expressed in Δ%/%) is shown graphically in FIG. 6 . In one aspect of a method according to the present disclosure, the choke characteristic flow Cv may be determined for the particular choke, that is, the choke 102 in FIG. 1 , with respect to the actual drilling fluid used to drill the well (FIG. 1 ).

The MPD control system (104 in FIG. 1 ) may comprise, e.g., in software operating on any form of computer or processor, a feed forward controller and a PID controller to ensure reliable pressure control while the MPD system is operating automatically. The feed forward controller is used to predict the optimal new choke opening in response to a change in determined or chosen (setpoint) well pressure, while the PID controller fine-tunes the choke opening to maintain a chosen target well pressure. This makes it possible to accommodate large pressure setpoint variations or determined pressure variations with only minimal overshoot in choke operation, and to substantially reduce the time needed for the MPD system to respond to a change in the setpoint pressure.

The PID controller may have different options available, for example, “Manual” PID selection where a static set of PID parameters is used, and “Automatic” PID selection where the operator can define two (or more) sets of PID parameters, dependent on the choke characteristics in low and high operating (opening) range. The most sophisticated models may use continuous PID parameter variations across the operating range. This will avoid the need for any manual retuning for large setpoint or determined well pressure step changes that would correspondingly require large step changes in choke opening.

For tuning the MPD control system (104 in FIG. 1 ), it is desirable to divide the tuning of the PID controller separately from the feed forward controller. However for both the PID and feed forward controllers, an accurate Cv curve is required and a good approximation of the well reaction should be known.

FIG. 7 is a graph illustrating a choke having an ordinary, non-linear Cv characteristic that may be used in a choke tuning example. As shown in FIG. 7 , the choke Cv may be approximated over the entire choke opening range by three different slopes A—[opening in the range of about 10%-45%], B—[opening in the range of about 45%-80%] and C—[opening in the range of about 80%-100%]. The system operator may choose which of the three choke opening ranges is of most interest during MPD system operation. If the MPD system is run with choke operating predominantly within the B,C opening range, then tuning can be best done in these ranges. Consequently, if the upper slope C is not considered important for pressure control, the system tuning may be performed with choke within opening ranges A, B.

Methods according to the present disclosure may be described by the following generalized procedures.

Fingerprinting procedure:

-   -   a. Determine actual choke parameters (fingerprinting Cv curve)     -   b. Determine the well characteristic (or process model as it is         described in MPD literature)

Feed forward controller procedure:

-   -   a. Calculate the required added (or removed) drilling         circulation system volume required to effect a specific well         pressure change     -   b. Operate the choke(s) (or increase/decrease pump rate)         closed/open to ensure a flow rate change.     -   c. Measure the corresponding drilling circulation system volume         changes     -   d. Move the choke(s) to the predetermined position based on         fingerprinted Cv (characterized choke) when the volume change         required has been reached.

PID Controller procedure:

-   -   a. Use the PID controller to stabilize the well pressure and         keep the well pressure at the chosen (desired) value using the         values found in the fingerprinting procedure

Actions needed to carry out the above procedures will be explained in more detail below.

Initial Characterization of Choke Response

The following actions may be undertaken when first initializing the MPD system on any specific well. Because every well may be different, that is, have a unique pressure response with respect to changes in drilling rig mud pump operating rate and choke position, it is desirable to perform the following steps at the start of drilling operations on any well or well section.

Using the choke manufacturer's initially provided Cv curve (e.g., see FIG. 5 ), by using the procedure in the following table it is possible to create a Cv curve, that is, the flow/choke %/pressure characterization for the specific choke (102 in FIG. 1 ) as actually used in the MPD system on the well being drilled. Maximum drilling fluid pressure and flow rates may be determined for any particular well. An example method for characterizing the flow/choke %/pressure, that is, determining the Cv curve, may be implemented according to the following table.

Step Activity 1. Activate choke in manual choke control mode and open 100%. 3. Run the mud pumps up to the maximum allowable flow according to the well construction plan 4. Close the active choke in 10% intervals from 100% to 70%. 5. At choke set points below 70%, decrease flow as per plan to the next 5% choke value before moving the choke to this value. 6. Optionally if the curve below 35% choke opening needs to be determined, decrease choke set points in 2% increments. 7. Ramp Down Mud Pumps and, open all chokes to 100% 8. Repeat the procedure for any other chokes in the system (if multiple chokes are present). 9. Use logged data points to create Cv table 10. If necessary re-adjust the Cv curve loaded in the system to match the measured curve

FIG. 8 shows a graph of an example embodiment of choke “fingerprinting”, wherein actual surface back pressure (SPB) with respect to flow rate and choke opening combinations are used to determined Cv values at different choke openings.

Determining Well Parameters

Determining the well parameters to be used in the PID controller can be a fast and easy to implement procedure. However, the system characteristic response of the combination of choke and well is related to the particular flow characteristics of both; therefore characterization should be repeated for every new well section (e.g., when a casing or liner is set and/or drill bit diameter changes) or if large changes in drilling operating parameters are encountered. For best results the characterization should be performed within the expected range of drilling operating parameters (mud flow rate, surface back pressure, mud weight, etc.). Also the well parameter determination has to be performed in expected operating region A, B or C of the Cv curve (see FIG. 7 ) in order for the right parameters to be entered into the PID controller.

The well parameter determination may be performed in manual choke control mode (i.e., with automatic control of the choke 102 disabled) and may comprise using predetermined steps in the choke opening. The surface back pressure (SBP) response is measured and will provide key inputs for determining optimal PID controller parameters. The steps in the table below may be performed in several different choke opening ranges to allow for the choke curve to be optimally covered.

Step Activity 1 Ensure the “Choke Cv curve” is configured in the control system. 2 Line up flow lines to one choke only. Close the inactive choke completely. 3 Set the MPD-CS in manual control mode and open the choke to the max of the first slope plus a margin and request the driller to slowly increase the pump speed. 4 Freeze the pump speed when a desired surface back pressure is reached. Let the system stabilize until flow in/flow out are the same, or with a fixed offset. 5 Manually close the choke in fixed increments and log the SBP (psi) and choke opening (%) over time. The system needs to stabilize between each step. 6 While in manual mode open the choke to the max of the second slope plus a margin and request the driller to slowly increase the pump speed. 7 Freeze the pump speed when a desired surface back pressure is reached. Let the system stabilize. 8 Manually close the choke in fixed increments and log the SBP (psi) and choke opening (%) over time. The system needs to stabilize between each step. 9 Repeat the above for any other chokes in the system and or any other regions of interest.

For the choke 102 (or each choke in a multiple choke MPD system) fill in the determined values in the following table using the graph and definitions in FIG. 9 as guidance for determining t_(choke), t_(SBP) and t_(S). The number of steps in any embodiment may be any chosen number. Note t_(SBP) is the first indication of the real pressure rise. It is not the time slope of the pressure curve.

Step Km (psi/%) Tm (sec) Sm (sec) $K_{m} = {\frac{{SBP}_{change}}{{Choke}_{change}}\frac{({psi})}{(\%)}}$ t_(SBP) − t_(choke) t_(s) − t_(SBP) 1 2 3 Average Region

Determining PID Controller Parameters

This step will provide the starting parameters for the PID controller. The starting parameter calculations may provide in most cases stable operation of the PID controller. This can be used as a basis to fine tune performance for specific situations. It has been determined that effective PID controller operation may be effected using three parameters, Km, Tm and Sm. Sm represents the time constant of the well, in essence how fast the well reacts to changes in choke setting. Tm represents time delay, that is, when the well starts reacting after a change in choke setting is made and Km represents the gain factor of the well and MPD system, that is, how the SBP changes as function of the choke opening change. It has been found that by empirically determining the foregoing three parameters, the MPD system can be made to operate reliably by the system operator without the need for guessing values of system operating parameters.

There are several different methods to calculate the PID parameters—each with its different characteristics. A spreadsheet as shown in the table below may be used to display the parameters when the Km, Tm and Sm values are filled in to populate the table. A good reference for determining proper parameters is “Handbook of PI and PID Controller Tuning Rules”, 3^(rd) edition, Aidan O'Dwyer.

Kp (controller proportional gain) Ti (controller integral time) Td Method (-) (s) (s) 1 $\frac{1}{K\_ m}\left( {{{0.6}939\frac{T\_ m}{S\_ m}} + {{0.\ 1}814}} \right)$ $\frac{{0{\text{.8647} \cdot T_{m}}} + {0{\text{.226} \cdot {S\_ m}}}}{\frac{T\_ m}{S\_ m} + {{0.8}647}}$ $\frac{0{\text{.0565} \cdot T_{m}}}{{{0.8}647\frac{T\_ m}{S\_ m}} + {{0.2}26}}$ 2 $\frac{0.6 \cdot {T\_ m}}{{K\_ m} \cdot {S\_ m}}$ T_m 0.5 · S_m 3 $\frac{0.95 \cdot {T\_ m}}{{K\_ m} \cdot {S\_ m}}$ 2.38 · S_m 0.42 · S_m

The following PID parameters combinations can be used as a starting point in case of the following example:

Km (psi/%) Tm (sec) Sm (sec) 0.47 5 5

Method Kp Ti(s) Td(s) 1 1.9 2.9 2.6 2 1.3 5 2.5 3 2 11.9 2.1

Determining the basic control parameters based on the step response of the system allows the definition of a stable set of PID parameters. These PID parameters can be used to further refine performance if needed. No knowledge of the well, mud properties or choke curves is required.

By tuning the functionality of the choke(s) in an MPD system according to the present disclosure, it is possible to accurately estimate a fluid volume necessary to add to or remove from the drilling circulation system (comprising the mud pump 22, drill pipe, casing 16, wellbore and annulus 24 in FIG. 1 ) in order to cause a predetermined change in the surface back pressure (SBP). Such estimation makes possible much more rapid MPD system response to changes in setpoint pressure. By way of example, increasing the setpoint pressure may be effected by substantial closure of the choke (102 in FIG. 1 ) for a determined time, after which the choke (102 in FIG. 1 ) is opened to a new fractional opening that will result in the SBP being substantially at the new setpoint. Corresponding opening of the choke may take place to effect a drop in the setpoint pressure. Accordingly, MPD system response using calibrated choke(s) according to the present disclosure may operate more quickly and therefore safely than using uncalibrated choke(s) controlled only by the PID controller or equivalent.

In light of the principles and example embodiments described and illustrated herein, it will be recognized that the example embodiments can be modified in arrangement and detail without departing from such principles. The foregoing discussion has focused on specific embodiments, but other configurations are also contemplated. In particular, even though expressions such as in “an embodiment,” or the like are used herein, these phrases are meant to generally reference embodiment possibilities, and are not intended to limit the disclosure to particular embodiment configurations. As used herein, these terms may reference the same or different embodiments that are combinable into other embodiments. As a rule, any embodiment referenced herein is freely combinable with any one or more of the other embodiments referenced herein, and any number of features of different embodiments are combinable with one another, unless indicated otherwise. Although only a few examples have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible within the scope of the described examples. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims. 

What is claimed is:
 1. A method for tuning a managed pressure drilling system comprising a variable orifice choke operating to controllably restrict fluid flow from a drilling well, the method comprising: (a) characterizing change in flow rate of fluid through the choke with respect to fractional choke opening at a substantially constant pressure drop across the choke; (b) characterizing change in fluid pressure in the well with respect to change in fractional choke opening at a substantially constant fluid flow rate into the well; (c) characterizing a response time of pressure in the well to changes in the fractional choke opening, a delay time of pressure response after a change in fractional choke opening and a surface back pressure applied to the well with respect to fractional choke opening; and using the characterizations in at least one of (a), and (b) and the characterization in (c) to calculate control parameters for a proportional integral differential controller having as a controlled output the fractional choke opening and as a control input the fluid pressure in the well before the choke.
 2. The method of claim 1 wherein the characterizing change in flow rate of fluid through the choke with respect to fractional choke opening at a substantially constant pressure drop across the choke comprises pumping fluid through a conduit extended into the well, measuring flow rate of fluid leaving the well through an annular space between the conduit and a wall of the well, measuring pressure of fluid in the well upstream of the choke, adjusting the fractional choke opening and changing a rate of the pumping fluid so that the measured pressure remains substantially constant.
 3. The method of claim 1 wherein the characterizing a response time of pressure in the well to changes in the fractional choke opening, a delay time of pressure response after a change in fractional choke opening and a surface back pressure applied to the well with respect to fractional choke opening comprises measuring pressure in the well upstream of the choke, measuring pressure upstream of the choke, and change in the measured pressure with respect to change in the fractional choke opening while pumping fluid into the well at a substantially constant rate.
 4. The method of claim 1 wherein the characterizing a response time of pressure in the well to changes in the fractional choke opening comprises measuring pressure in the well upstream of the choke with respect to time, and determining an elapsed time between change in the fractional choke opening and a change in the measured pressure while pumping fluid into the well at a substantially constant rate. 